CNC machine tools typically control cutter paths during the machining process. For sake of convenience, users may usually work out a machining program according to the contours of a workpiece to derive a programmed path, and the desired cutter path can be obtained by offsetting the programmed path by one radius of the cutter. The function of a numerical device being capable of automatically generating the cutter path in real time is often referred to as the cutter path planning function. Regarding two respective curves (i.e., the programmed path) belonging to different planes when performing the cutter path planning in a three-dimensional space, due to the inconsistency between the spatial normal vectors of the curves at their transition point (the intersection of the two curves), the resultant cutter paths corresponding to the two curves may not be on the same plane, that is, the cutter paths may not have an intersection.
Referring to FIG. 1, in which mk and kn are two programmed paths in a three-dimensional space, m1k1 is a corresponding cutter path of mk, whilst k2n1 is a corresponding cutter path of kn, and m1k1 and k2n1 are skew lines as they lie in separate planes. Further, G1 is the cutter radius compensation plane of mk and G2 is the cutter radius compensation plane of kn, G1 and G2 intersecting in line OU. And mk and OU form an angle α>90°, kn and OU form an angle β>90°, and α≤β. A prior art method for cutter path planning at the transition part of two programmed paths may comprise: finding a point k1′ on line m1k1, ensuring kk1′=r, wherein r is the radius of the cutter, point k1′ is a transition point, and the machining path order for the cutter is m1k1′→k1′k2→k2n1.
Applicant of the present disclosure, however, has found in long-term research and development that in the prior art cutter path planning method the distance from the transition point k1′ to the programmed path kn is smaller than the radius r of the cutter, such that when machining a workpiece, the part that shouldn't be processed may be cut off, thus leading to over-cutting issues.